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We numerically demonstrated the generation of terahertz-mid-infrared (THz-MIR) anisotropic vortex beams from few-cycle vortex-laser-induced air plasma based on both the intra-pulse four-wave mixing and the photocurrent models. It is found that for the low-frequency THz components, their phase variance on the azimuthal angle follows a simple stepwise increase with a step of π, indicating the unsuccessful inheritance of the orbital angular momentum (OAM) from the few-cycle vortex driving laser. However, for the high-frequency MIR components, they are anisotropic vortex beams with a nonlinear variance in the phase profile showing angular acceleration, which indicates they carry OAM. Also, their intensity distributions vary from two-petal structure slowly to ring-shaped structure as the frequency increases. Physically, the behaviors of their phase and intensity distributions can be explained well by the interference theory of the two models. Interestingly, according to the fitting formula of the phase distributions, the calculated topological charges (TCs) of all components in the THz-MIR frequencies range are equal to that of the driving laser. Moreover, the phase nonlinearity and the intensity distributions strongly depend on the corresponding THz-MIR frequencies. The results from both schemes are the decoupling of the OAM, the TC, the geometry and the power distribution in anisotropic vortex beams.

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